1. The notions norm and trace were originally introduced in German language as “die Norm” and “die Spur”. Therefore in German and many other literature the symbol of trace is S, Sp or sp. Nowadays the symbols T and Tr are common.

2. The norm and trace of an algebraic numberαα\alpha in the field extension ℚ⁢(α)/ℚℚαℚ\mathbb{Q}(\alpha)/\mathbb{Q}, i.e. the product and sum of all algebraic conjugates of αα\alpha, are called the absolute norm and the absolute trace of αα\alpha. Formulae like (1) concerning the absolute norms and traces are not sensible.